First colonization of a hard-edge in random matrix theory
Mathematical Physics
2008-04-08 v1 math.MP
Abstract
We describe the spectral statistics of the first finite number of eigenvalues in a newly-forming band on the hard-edge of the spectrum of a random Hermitean matrix model. It is found that in a suitable scaling regime, they are described by the same spectral statistics of a finite-size Laguerre-type matrix model. The method is rigorously based on the Riemann-Hilbert analysis of the corresponding orthogonal polynomials.
Cite
@article{arxiv.0804.1111,
title = {First colonization of a hard-edge in random matrix theory},
author = {M. Bertola and S. Y. Lee},
journal= {arXiv preprint arXiv:0804.1111},
year = {2008}
}
Comments
22 pages, 7 figures